{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_cost(x, y, w, b):\n",
    "  m = x.shape[0]\n",
    "  j_wb = 0\n",
    "  for i in range(m):\n",
    "    f_wb = w*x[i] + b\n",
    "    j_wb += (f_wb - y[i]) ** 2\n",
    "  \n",
    "  j_wb = j_wb * (1/2*m)\n",
    "\n",
    "  return j_wb\n",
    "\n",
    "def linear_regression_line(x, w, b):\n",
    "  m=df.shape[0]\n",
    "  f_wb = np.zeros(m)\n",
    "  for i in range(m):\n",
    "    f_wb[i] = w*df['YearsExperience'][i] + b\n",
    "\n",
    "  return f_wb\n",
    "\n",
    "def compute_gradient(x, y, w, b):\n",
    "  dj_dw = 0\n",
    "  dj_db = 0\n",
    "\n",
    "  for i in range(len(x)):\n",
    "    f_wb = w * x[i] + b\n",
    "    dj_dw_i = (f_wb - y[i]) * x[i]\n",
    "    dj_db_i = f_wb - y[i]\n",
    "    dj_dw += dj_dw_i\n",
    "    dj_db += dj_db_i\n",
    "  \n",
    "  dj_dw = dj_dw * (1/len(x))\n",
    "  dj_db = dj_db * (1/len(x))\n",
    "\n",
    "  return dj_dw, dj_db\n",
    "\n",
    "def gradient_descent(x, y, w, b, alpha, num_iter, cost_function, gradient_function):\n",
    "  J_history = []\n",
    "  w_history = []\n",
    "  b_history = []\n",
    "  \n",
    "  for i in range(num_iter):\n",
    "    dj_dw, dj_db = gradient_function(x, y, w, b)\n",
    "    w = w - alpha * dj_dw\n",
    "    b = b - alpha * dj_db\n",
    "\n",
    "    if i<100000:\n",
    "      J_history.append(cost_function(x, y, w, b))\n",
    "      w_history.append(w)\n",
    "      b_history.append(b)\n",
    "    \n",
    "    if i% math.ceil(num_iter/10) == 0:\n",
    "      print(f\"Iteration {i} for parameters w = {w} and b = {b}, cost is: {J_history[-1]:0.2e}\")\n",
    "      print(f\"Gradient is {dj_dw:0.3e} for w and {dj_db:0.3e} for b\")\n",
    "  \n",
    "  return w, b, J_history, w_history, b_history"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv('Salary_dataset.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>YearsExperience</th>\n",
       "      <th>Salary</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>1.2</td>\n",
       "      <td>39344.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1.4</td>\n",
       "      <td>46206.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>1.6</td>\n",
       "      <td>37732.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>2.1</td>\n",
       "      <td>43526.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>2.3</td>\n",
       "      <td>39892.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Unnamed: 0  YearsExperience   Salary\n",
       "0           0              1.2  39344.0\n",
       "1           1              1.4  46206.0\n",
       "2           2              1.6  37732.0\n",
       "3           3              2.1  43526.0\n",
       "4           4              2.3  39892.0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 0 for parameters w = 4850.044133333334 and b = 760.04, cost is: 1.17e+12\n",
      "Gradient is -4.850e+05 for w and -7.600e+04 for b\n",
      "Iteration 1000 for parameters w = 9879.928601219774 and b = 21918.621894264932, cost is: 1.49e+10\n",
      "Gradient is 8.854e+01 for w and -6.033e+02 for b\n",
      "Iteration 2000 for parameters w = 9504.92118565751 and b = 24473.740872888877, cost is: 1.41e+10\n",
      "Gradient is 1.132e+01 for w and -7.711e+01 for b\n",
      "Iteration 3000 for parameters w = 9456.987236888157 and b = 24800.339593709716, cost is: 1.41e+10\n",
      "Gradient is 1.447e+00 for w and -9.856e+00 for b\n",
      "Iteration 4000 for parameters w = 9450.86025552919 and b = 24842.085878455833, cost is: 1.41e+10\n",
      "Gradient is 1.849e-01 for w and -1.260e+00 for b\n",
      "Iteration 5000 for parameters w = 9450.077096587838 and b = 24847.421944334237, cost is: 1.41e+10\n",
      "Gradient is 2.363e-02 for w and -1.610e-01 for b\n",
      "Iteration 6000 for parameters w = 9449.97699216586 and b = 24848.104007402384, cost is: 1.41e+10\n",
      "Gradient is 3.021e-03 for w and -2.058e-02 for b\n",
      "Iteration 7000 for parameters w = 9449.964196684927 and b = 24848.191189614834, cost is: 1.41e+10\n",
      "Gradient is 3.862e-04 for w and -2.631e-03 for b\n",
      "Iteration 8000 for parameters w = 9449.962561149461 and b = 24848.20233336169, cost is: 1.41e+10\n",
      "Gradient is 4.936e-05 for w and -3.363e-04 for b\n",
      "Iteration 9000 for parameters w = 9449.962352093133 and b = 24848.2037577703, cost is: 1.41e+10\n",
      "Gradient is 6.309e-06 for w and -4.299e-05 for b\n"
     ]
    }
   ],
   "source": [
    "iterations = 10000\n",
    "tmp_alpha = 1.0e-2\n",
    "\n",
    "w, b, J_hist, w_hist, b_hist = gradient_descent(df['YearsExperience'], df['Salary'], 0, 0, tmp_alpha, iterations, compute_cost, compute_gradient)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimated salary for 10 years of experience is 119347.83\n"
     ]
    }
   ],
   "source": [
    "years_exp = 10\n",
    "est_salary = w * years_exp + b\n",
    "print(f\"Estimated salary for {years_exp} years of experience is {est_salary:0.2f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.set_style('darkgrid')\n",
    "plt.plot(J_hist, color='blue')\n",
    "plt.xlabel('Iterations')\n",
    "plt.ylabel('Cost')\n",
    "plt.title('Cost vs Iterations')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 4000x4000 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.set_style('darkgrid')\n",
    "axis = plt.axes(projection='3d')\n",
    "axis.plot3D(w_hist, b_hist, J_hist)\n",
    "plt.title('Cost vs Parameters')\n",
    "plt.figure(figsize=(40, 40))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
